In [1]}, the QAOA approach was generalized to the Quantum Alternating Operator Ansatz, considering unitary layers that are not necessarily linked to local Hamiltonian evolution. In particular, multi-qubit mixing operators were introduced in lieu of the \(X\) -rotations when applying the QAOA to hard-constrained optimization in order to restrict the search to the feasible subspace, the space of valid configurations obeying the hard constraints.
The simplest among the advanced mixers is the two-qubit XY gate
\(\mathcal {U}^{nm}_{XY}(\beta )=\exp \left[i\beta (X_n X_m +Y_n Y_m)\right]\) 
